8.2.6. transitionModelSolver

The laminar to turbulence transition model supported by Flow360 is the 2019b version of the Amplification Factor Transport (AFT) model created by James Coder, University of Tennessee. This model adds two additional equations to the flow solver in order to solve for the amplification factor and intermittency flow quantities. More details about the model can be found here. Below are a list of configuration parameters for the transition model. Either Ncrit or turbulenceIntensityPercent can be used to tune the location of transition from laminar to turbulent flow.

8.2.6.1. absoluteTolerance

The absoluteTolerance is the primary convergence metric for steady cases. At least 5 orders of magnitude reduction is recommended for all residual values. The absoluteTolerance can also be used for unsteady cases, but is less meaningful than the relativeTolerance, as the initial residual values change between different physical steps.

8.2.6.2. relativeTolerance

The relative residual is defined as the ratio of the current pseudoStep’s residual to the maximum residual present in the first 10 pseudoSteps within the current physicalStep. When running unsteady cases, the relativeTolerance is typically set to 1e-2 or 1e-3. Once the nonlinear residuals drop by 2 or 3 orders of magnitude, the solver will continue to the next physicalStep. The relativeTolerance is ignored for steady cases.

8.2.6.3. orderOfAccuracy

As recommended in the orderOfAccuracy of navierStokesSolver, when solving unsteady cases, it may be necessary to initialize the flow field with orderOfAccuracy set to 1. Once the flow field has been initialized, the user can create a child case and switch the orderOfAccuracy back to 2.

When adjusting the orderOfAccuracy for the transitionModelSolver, the navierStokesSolver and turbulenceModelSolver should be adjusted as well.

8.2.6.4. linearSolverConfig

The transition solver is typically easier to converge than the NS solver. Therefore, the value of maxIterations for the transition solver, typically set to ~20, is less than maxIterations for the NS solver. However, if the linear residual reduction ratio after linear solver is not enough, increasing maxIterations up to ~50 could be helpful. The default maxIterations for transition solver is 20.

8.2.6.5. updateJacobianFrequency

Similar to the NS solver, the default value for updateJacobianFrequency is 4, indicating that the Jacobian for evaluating the transition equations is only updated every 4 pseudo-steps. For more challenging cases, updateJacobianFrequency may need to be reduced from 4 to 1. This will not significantly slow down the solver, since the transition equation is not as computationally expensive as the NS equation.

8.2.6.6. equationEvalFrequency

As mentioned above, the transition equation is typically easier to converge than the NS equations. Therefore, by default, equationEvalFrequency is set to 4, meaning that the transition equation is only evaluated every 4 pseudo-steps. For challenging cases, equationEvalFrequency may need to be reduced from 4 to 1 as well. This change will not significantly impact the solver’s performance.

8.2.6.7. Ncrit

Ncrit is the critical amplification factor. Boundary layer transition is triggered when the amplified frequency of the Tollmien-Schlichting waves reaches this value. Higher values delay the onset of laminar-turbulent transition. Only Ncrit or turbulenceIntensityPercent, can be specified in the flow configuration file. The value has a range of 1 to 11 in Flow360.

8.2.6.8. turbulenceIntensityPercent

turbulenceIntensityPercent is used to compute the Ncrit parameter (see above) for the AFT transition model using: \(N_{crit} = -8.43 - 2.4 ln (0.025*tanh(\text{turbulenceIntensityPercent})/2.5)\). Higher values of turbulenceIntensityPercent therefore lead to earlier transition. The value of turbulenceIntensityPercent has a range of 0.03 to 2.5 (%) in Flow360.